A Plausible Path Towards Unification of Interactions via Gauge Fields Consistent with the Equivalence Principle-II

Abstract

An extension of the Lorentz group that includes generators $\Gamma^\mu$ carrying a space-time index has been previously demonstrated to \emph{explicitly} construct the Minkowski metric \emph{within} the internal group space as a consequence of the non-vanishing commutation relations between those generators. Fields that transform under representations of this extended group can fundamentally incorporate microscopic causality as a crucial property of physical fields. The first part of this exploration focused on the fundamental representation fermions (which satisfy the Dirac equation), and explored additional internal symmetries associated with those fermions. Any interactions that could result from those symmetries were demonstrated to necessarily be consistent with gravitational equivalence under curvilinear extensions of the (abelian) space-time translations. The first boson representation of this algebra is the focus of this second paper. In particular, the equations of motion for a group of massive vector bosons are degenerate with that of massless vector bosons, allowing them to unitarily mix to form physical states with differing masses and dynamics. Thus, this representation exhibits a potential for enhancing insights into the standard modeling of electro-weak mixing of bosons. The various spinors that represent these bosons exhibit kinematic factors, and those factors are related during unitary mixing to generate the resultant physical states. For this reason, analytic and kinematic coincidences associated with known electro-weak masses will be explored for insights into possible predictive relationships between their masses and those of this first causal boson representation. To conclude, a plausible model will be constructed using examined coincidences for critique and insights into the potential viability of the approach.